(3x-1)(x)/2=22

Solution for (3x-1)(x)/2=22 equation:

(3x-1)(x)/2=22

We move all terms to the left:

(3x-1)(x)/2-(22)=0

We multiply all the terms by the denominator


(3x-1)x-22*2=0

We add all the numbers together, and all the variables

(3x-1)x-44=0

We multiply parentheses

3x^2-1x-44=0

a = 3; b = -1; c = -44;
Δ = b2-4ac
Δ = -12-4·3·(-44)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-23}{2*3}=\frac{-22}{6}
=-3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+23}{2*3}=\frac{24}{6}
=4
$